Final answer:
The probability of drawing a card greater than a five and less than a nine from a standard 52-card deck is 3/13, as there are 12 such cards out of the total 52 cards.
Step-by-step explanation:
When we wish to calculate the probability of drawing a card greater than five and less than nine from a standard 52-card deck, we are looking at a specific range of cards in each suit. These cards are the 6, 7, and 8 from each of the four suits. Since each suit has one of these cards, there are 3 cards per suit that meet the criteria and therefore, a total of 3 cards * 4 suits = 12 cards that satisfy our condition out of the 52 total cards.
To find the probability, we use the formula for probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Substituting the numbers we get:
- Number of favorable outcomes = 12 (6, 7, and 8 from each suit)
- Total number of possible outcomes = 52 (total cards in the deck)
Therefore:
Probability = 12 / 52
We can simplify this fraction by dividing both the numerator and the denominator by 4, which gives us:
Probability = 3 / 13
The probability of drawing a card that is greater than five and less than nine is thus 3/13.